Diffraction-Based Overlay Metrology System Design

In the semiconductor industry, the alignment of the different layers used in lithography is essential. Overlay metrology systems allow to measure the eventual misalignment (overlay) that can happen during manufacturing. In this example, we demonstrate how to model a complete diffraction-based overlay metrology system ― from the illumination through the diffraction grating to the collection ― and how to estimate the measurement accuracy through overlay calculation. The nano-scale targets are designed with Ansys Lumerical RCWA and the lens system is modeled in Ansys Zemax OpticStudio, while leveraging the dynamic link between RCWA and OpticStudio workflow and optimization.

download example

Software Prerequisites

To be able to use this Example, the following tools and assets need to be installed on your computer:

• Ansys Lumerical RCWA 2024 R1 or later
• Ansys Zemax OpticStudio 2023 R2 or later
• The Lumerical RCWA Dynamic Link from OpticStudio requires an Ansys Zemax OpticStudio Premium or Enterprise license

Overview

Understand the simulation workflow and key results

With the reduction of semiconductor device feature size in integrated circuit, the alignment of the different layers is critical and the offset or overlay between layers must be kept minimal. Manufacturers spend a considerable amount of their control budget in overlay metrology, while system designers must increase the measurement accuracy to match the industry needs.

ls -

Among various overlay measurement methods, the ones based on multiple gratings (diffraction based overlay metrology) provide better accuracy than those based on imaging systems. The grating parameters (target size, pitch, fill factor, intentional offset) and beam parameters (spot size, angle of incidence) have to be chosen carefully to ensure the desired accuracy.

In this example, we will use the differential signal method (see Appendix) and calculate the overlay from the reflected signals (0th order) of 4 targets.

Step 1: Modelling diffraction grating structure in Ansys Lumerical RCWA

The first step is to implement in Lumerical the grating-over-grating structure used for diffraction-based overlay measurements. Based on this nano-scale model, light interaction with the gratings can be accurately simulated to calculate the diffraction angles and diffraction efficiency.

Using the RCWA solver, we can calculate the fraction of power reflected in the 0th order as a function of the overlay, for 4 targets designed with an intentional offset. By varying the angle of incidence, we can determine the optimum angle to get the best accuracy for the overlay estimation.

Step 2: Modelling illumination and collection system in Ansys Zemax OpticStudio

As a next step, the entire illumination and collection measurement system is modelled in OpticStudio, including the source, macro-scale lenses, apertures, and detectors. In this example, we use a paraxial model with Köhler illumination, to demonstrate how to set up the system and vary the measurement parameters. We use the Dynamic Link between Lumerical RCWA and OpticStudio, allowing to control all the simulation parameters in OpticStudio.

Step 3: Calculating overlay in Python post-processing

Finally, the overlay is calculated by a differential signal approach based on multiple test results with different targets. To fully automate the procedure, subsequent simulations with different targets are run from the API, and the results are post-processed and visualized in Python as well.

Run and Results

Instructions for running the model and discussion of key results

Step 1: Modelling diffraction grating structure in Ansys Lumerical RCWA

1. Open the file DBO_simulation_2D_RCWA_dynamic.fsp in Lumerical FDTD and check the simulation settings.
2. Open the script file calculate_overlay.lsf in Lumerical FDTD script file editor and check the script settings.
3. Run the script.

The script will set up the 4 targets, using an intentional offset of \(F+f_0\), \(-F + f_0\), \(F – f_0\) and \(-F-f_0\) (with \(F=50nm\) and \(f_0=16nm\), see Appendix), sweep over the overlay and calculate the grating orders at different angles of incidence (from 0° to 80°) using the RCWA solver.

The image below shows the geometry as defined in Lumerical RCWA.

It will then extract the reflected signal (0th order) and calculate the overlay from the differential signal. Finally, the script calculates the error (difference between the overlay set in the simulation and the one calculated from the reflected signals).

The following plots show the calculated overlay and error for normal incidence (theta=0°) and 45° incidence (theta=45°).

To obtain these plots, set “do_plot” to true, and set theta_target to the desired value.

The simulation results show the best accuracy is obtained for an angle of incidence of 45°, with an error smaller than 0.01nm.

Note the simulation file is already set to be used in OpticStudio via the dynamic link.

Step 2: Modelling illumination and collection system in Ansys Zemax OpticStudio

1. Open the DBO_fullSystem_Kohler_paraxial_filter_final.zprj file in OpticStudio and observe the full system setup.2.
2. On the Diffraction Grating object under the Diffraction Properties, set the Link Lumerical parameter to 1.
3. Update the NSC 3D Layout to visualize the diffracted rays after the overlay target.
4. Open the Ray Trace Control and Clear & Trace rays with Use Polarization, Split NSC Rays, and Ignore Errors checked on.

Now that we have implemented the grating-over-grating target in Lumerical, we can utilize this model and place it inside the whole macro-scale measurement setup, including both the illumination and the collection systems. In order to improve the accuracy of the overlay measurements, uniform illumination is required on the target, therefore we use a Köhler illumination system. In this type of setup, the source is imaged onto the pupil plane at back focal plane of the objective lens, and the illuminated target size is defined by the size of the field stop.

In this example, we use a simplified paraxial Köhler illumination system to demonstrate the working principle and showcase how to adjust the illumination settings. We model the typical illumination aperture in the system by a Source Point object, which emits rays into a cone with uniform distribution. This Source Point is imaged onto the pupil plane, at the back focal plane of the objective lens, and therefore its X/Y position defines the illumination angle for the measurement. Based on the previous test results, we use 45° angle of incidence to improve the overlay accuracy.

The relay lenses in the illumination setup are modeled by Paraxial Lens objects, and the field stop at the conjugate plane is represented by an Annulus. The Minimum X/Y Half Widths of the field stop Annulus define the illumination size, and therefore these parameters are set based on the magnification of the system to illuminate the target structure, with a beam size of 5 um radius.

The following images show the signal recorded by the detector (left - spatial distribution, right – angular distribution).

The Si substrate of the overlay target is represented by a Rectangular Volume object, and the grating-over-grating overlay target is modeled by a Diffraction Grating object, where the Diffraction Properties are obtained by the lumerical-sub-wavelength-dynamic-link-2023R2.dll via the Dynamic Link to Lumerical RCWA. The previously generated DBO_simulation_2D_RCWA_dynamic.fsp file is set under File Name to define the connection to accurately simulate diffraction from the nano-scale structure.

Similarly to the illumination system, the collection part is also modeled by a simplified paraxial setup. It consists of two relay lenses, which re-image the pupil plane to the final detector. Additionally, an extra filter aperture is added in front of the detector, to select the analyzed diffraction order and block all the other unwanted orders. In this example, we use only the zeroth order diffraction signal in our analyses. Finally, the total power of the selected diffraction signal is measured on the final detector.

Here, the total power recorded by the detector is 0.46W.

Step 3: Calculating overlay by Python post-processing

1. Observe how the Merit Function is set up in the DBO_fullSystem_Kohler_paraxial_filter_final.zprj Zemax file to run a ray trace and collect data from the detectors.
2. Open the PythonZOSConnection_overlayCalculation.py file in a Python IDE, and check the automation script to see how it adjusts the grating parameters and runs simulations in a loop with different settings.
3. Under the Programming tab of OpticStudio, click the Interactive Extension button to set OpticStudio to wait for API connection.
4. Run the PythonZOSConnection_overlayCalculation.py file to start the automated simulation.

As a last step, we extract the overlay value from the measured signals and estimate its accuracy. In this example, we apply the zeroth order methodology, which means that four different targets are tested with four different intentional offsets: \(F+f_0\), \(-F+f_0\), \(F-f_0\), and \(-F-f_0\) (see Appendix).

In order to simulate this overlay measurement procedure, the target structure has to be adjusted by setting different intentional offset parameters for the subsequent tests. Once the macro-scale Zemax system setup is linked to the nano-scale Lumerical grating-over-grating structure via the RCWA Dynamic Link, all the settings can be modified from OpticStudio. On the Diffraction Grating, parameter #6, D, sets the intentional offset, while parameter #7, epsx, sets the overlay.

To fully automate the simulation process, the grating-over-grating target setup is adjusted from the Python ZOS-API to mimic different intentional offsets, and the subsequent tests on the different targets are also run from the API. The measurement signal, i.e. the total power on the final detector, is extracted from the Merit Function using the NSDD Non-Sequential Detector Data optimization operand. Finally, the detector data are post-processed to calculate the overlay and the results visualized as well. For each target, multiple preset overlay values are simulated, and the measurement accuracy is estimated based on the difference of the preset and calculated overlays.

The script will generate 2 plots (see below – calculated overlay and error on overlay calculation) and will save the results in a text file.

With a maximum error of 0.02nm, the results are consistent with the ones obtained using RCWA only (step 1).

Important Model Settings

Description of important objects and settings used in this model

Lumerical RCWA simulation

The simulation file DBO_simulation_2D_RCWA_dynamic.fsp is set for the Dynamic workflow between Lumerical RCWA and Zemax OpticStudio . The grating structure is set in the “topcell” structure group so its properties can be used in OpticStudio:

Non-Sequential ray trace settings in OpticStudio

To achieve high accuracy overlay calculations with the simulations, apply the following ray termination criteria under the System Explorer > Non-Sequential settings in OpticStudio.

Updating the Model With Your Parameters

Instructions for updating the model based on your device parameters

Grating

In this example, the grating structure is parametrized. You can modify the parameters in the “topcell” structure group:

• Period, refractive indices, fill factor of each grating, layer thicknesses

Target definition:

The targets are defined based on the intentional offset parameters, \(F\) and \(f_0\) (for 0th order scatterometry). These parameters can be modified in the scripts.

Macro-scale optical system

This example uses a Köhler illumination setup, where the illumination angle and size can be adjusted independently by finetuning the source position and field stop size, respectively. To do so, the X/Y Position of the Source Point, and the Minimum X/Y Half Width of the field stop Annulus can be easily adjusted in the Non-Sequential Component Editor in OpticStudio. Similarly, the position and the focal length of the applied Paraxial Lens objects can be customized from the NSC Editor if the system needs to be updated.

Taking the Model Further

Information and tips for users that want to further customize the model

Optimizing the grating

In this example, we consider a rectangular shaped grating. Other shapes can be used to optimize the system.

In a similar way, a more complex stack can be used.

Custom illumination and collection system design

The current example uses a simplified paraxial illumination and collection system to demonstrate the schematic workflow with the entire measurement setup. For custom applications, more realistic customized system models can be implemented. The paraxial lenses can be replaced with real stock or even with purposely optimized lenses to take aberrations in the system into account.

First order scatterometry

In this example, we calculate the overlay and estimate its error in case of zeroth order scatterometry, however, the same system setup (presented in the first two steps), can be used for first order scatterometry as well (see Appendix). This requires adapting the scripts as well as the grating structure for optimum results.

Additional Resources

Additional documentation, examples and training material

Related Publications

1. M. Adel, D. Kandel, V. Levinski, J. Seligson, A. Kuniavsky, Diffraction order control in overlay metrology: a review of the roadmap options, Proceedings of SPIE, 6922, Metrology, Inspection, and Process Control for Microlithography XXII, 692202 (2008).
2. Y. Shi, K. Li, X. Chen, P. Wang, H. Gu, H. Jiang, C. Zhang, S. Liu, Multiobjective optimization for target design in diffraction-based overlay metrology, Applied Optics, 59(9):2897-2905 (2020).
3. A. J. d. Boef, Optical wafer metrology sensors for process-robust CD and overlay control in semiconductor device manufacturing, Surface Topography: Metrology and Properties 4, 023001 (2016).
4. M. Ebert, H. Cramer, W. Tel, M. Kubis, H. Megens, Combined overlay, focus and CD metrology for leading edge lithography, Proc. SPIE 7973, Optical Microlithography XXIV, 797311 (2011).
5. Y. J. Sohn, B. M. Barnes, L. Howard, R. M. Silver, R. Attota, M. T. Stocker, Köhler illumination for high-resolution optical metrology, Proceedings of SPIE, 6152, Metrology, Inspection, and Process Control for Microlithography XX, 61523S (2006).

See Also

• RCWA Solver Introduction
• Dynamic workflow between Lumerical RCWA and Zemax OpticStudio
• DLL: dynamic Link RCWA (Zemax Community)

Related Ansys Innovation Courses

Appendix

Additional background information and theory

Differential signal scatterometry

The differential signal approach consists of measuring 4 signals reflected from pre-defined targets and combining them to calculate the overlay. These signals can be the reflected 0th order, or +1/-1st orders.
The algorithms and target design are different for zeroth or first order scatterometry, since for the zeroth order one target gives a single signal, while for the first order two signals, both the +/- first orders can be used for every target.

0th order:

Here we use 4 targets defined with an intentional offset, \(F+f_0\), \(-F+f_0\), \(F-f_0\), and \(-F-f_0\). Then, the power of the reflected light into the zeroth order is recorded as the signal \(S_1\), \(S_2\), \(S_3\), and \(S_4\), respectively.

Based on these results, the overlay \(\varepsilon\) is calculated using the following equations.

$$ D_1 = S_1 - S_2 $$

$$ D_2 = S_3 - S_4 $$

$$ \varepsilon = f_0 \frac{D_1 + D_2}{D_1 - D_2} $$

1st order

Here we use 2 targets defined with an intentional offset, \(f_0\) and \(-f_0\).

The measured signals will be the power of the reflected light into the plus and minus first orders, \(S_1^{+1}\), \(S_1^{-1}\), \(S_2^{+1}\) and \(S_2^{+1}\), respectively. Finally, from these results, the overlay \(\varepsilon\) is computed using the following equations

$$ D_1 = S_1^{+1} - S_1^{-1} $$

$$ D_2 = S_2^{+1} - S_2^{-1} $$

$$ \varepsilon = f_0 \frac{D_1 + D_2}{D_1 - D_2} $$